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2011 On the one-sided exit problem for fractional Brownian motion
Frank Aurzada
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Electron. Commun. Probab. 16: 392-404 (2011). DOI: 10.1214/ECP.v16-1640

Abstract

We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some light on the relation to the quantity I studied there.

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Frank Aurzada. "On the one-sided exit problem for fractional Brownian motion." Electron. Commun. Probab. 16 392 - 404, 2011. https://doi.org/10.1214/ECP.v16-1640

Information

Accepted: 9 August 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1244.60042
MathSciNet: MR2831079
Digital Object Identifier: 10.1214/ECP.v16-1640

Subjects:
Primary: 60G22
Secondary: (60G15 , 60G18)

Keywords: First passage time , fractional Brownian motion , Lower tail probability , One-sided barrier problem , One-sided exit problem , small value probability , Survival exponent

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